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Polytope of Type {2,112,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,112,2,2}*1792
if this polytope has a name.
Group : SmallGroup(1792,1076043)
Rank : 5
Schlafli Type : {2,112,2,2}
Number of vertices, edges, etc : 2, 112, 112, 2, 2
Order of s0s1s2s3s4 : 112
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,56,2,2}*896
   4-fold quotients : {2,28,2,2}*448
   7-fold quotients : {2,16,2,2}*256
   8-fold quotients : {2,14,2,2}*224
   14-fold quotients : {2,8,2,2}*128
   16-fold quotients : {2,7,2,2}*112
   28-fold quotients : {2,4,2,2}*64
   56-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  4,  9)(  5,  8)(  6,  7)( 11, 16)( 12, 15)( 13, 14)( 17, 24)( 18, 30)
( 19, 29)( 20, 28)( 21, 27)( 22, 26)( 23, 25)( 31, 45)( 32, 51)( 33, 50)
( 34, 49)( 35, 48)( 36, 47)( 37, 46)( 38, 52)( 39, 58)( 40, 57)( 41, 56)
( 42, 55)( 43, 54)( 44, 53)( 59, 87)( 60, 93)( 61, 92)( 62, 91)( 63, 90)
( 64, 89)( 65, 88)( 66, 94)( 67,100)( 68, 99)( 69, 98)( 70, 97)( 71, 96)
( 72, 95)( 73,108)( 74,114)( 75,113)( 76,112)( 77,111)( 78,110)( 79,109)
( 80,101)( 81,107)( 82,106)( 83,105)( 84,104)( 85,103)( 86,102);;
s2 := (  3, 60)(  4, 59)(  5, 65)(  6, 64)(  7, 63)(  8, 62)(  9, 61)( 10, 67)
( 11, 66)( 12, 72)( 13, 71)( 14, 70)( 15, 69)( 16, 68)( 17, 81)( 18, 80)
( 19, 86)( 20, 85)( 21, 84)( 22, 83)( 23, 82)( 24, 74)( 25, 73)( 26, 79)
( 27, 78)( 28, 77)( 29, 76)( 30, 75)( 31,102)( 32,101)( 33,107)( 34,106)
( 35,105)( 36,104)( 37,103)( 38,109)( 39,108)( 40,114)( 41,113)( 42,112)
( 43,111)( 44,110)( 45, 88)( 46, 87)( 47, 93)( 48, 92)( 49, 91)( 50, 90)
( 51, 89)( 52, 95)( 53, 94)( 54,100)( 55, 99)( 56, 98)( 57, 97)( 58, 96);;
s3 := (115,116);;
s4 := (117,118);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(118)!(1,2);
s1 := Sym(118)!(  4,  9)(  5,  8)(  6,  7)( 11, 16)( 12, 15)( 13, 14)( 17, 24)
( 18, 30)( 19, 29)( 20, 28)( 21, 27)( 22, 26)( 23, 25)( 31, 45)( 32, 51)
( 33, 50)( 34, 49)( 35, 48)( 36, 47)( 37, 46)( 38, 52)( 39, 58)( 40, 57)
( 41, 56)( 42, 55)( 43, 54)( 44, 53)( 59, 87)( 60, 93)( 61, 92)( 62, 91)
( 63, 90)( 64, 89)( 65, 88)( 66, 94)( 67,100)( 68, 99)( 69, 98)( 70, 97)
( 71, 96)( 72, 95)( 73,108)( 74,114)( 75,113)( 76,112)( 77,111)( 78,110)
( 79,109)( 80,101)( 81,107)( 82,106)( 83,105)( 84,104)( 85,103)( 86,102);
s2 := Sym(118)!(  3, 60)(  4, 59)(  5, 65)(  6, 64)(  7, 63)(  8, 62)(  9, 61)
( 10, 67)( 11, 66)( 12, 72)( 13, 71)( 14, 70)( 15, 69)( 16, 68)( 17, 81)
( 18, 80)( 19, 86)( 20, 85)( 21, 84)( 22, 83)( 23, 82)( 24, 74)( 25, 73)
( 26, 79)( 27, 78)( 28, 77)( 29, 76)( 30, 75)( 31,102)( 32,101)( 33,107)
( 34,106)( 35,105)( 36,104)( 37,103)( 38,109)( 39,108)( 40,114)( 41,113)
( 42,112)( 43,111)( 44,110)( 45, 88)( 46, 87)( 47, 93)( 48, 92)( 49, 91)
( 50, 90)( 51, 89)( 52, 95)( 53, 94)( 54,100)( 55, 99)( 56, 98)( 57, 97)
( 58, 96);
s3 := Sym(118)!(115,116);
s4 := Sym(118)!(117,118);
poly := sub<Sym(118)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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